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Memories of Professor Hiroshi Kunita 国田宏教授的回忆
Journal of Stochastic Analysis Pub Date : 2021-08-10 DOI: 10.31390/josa.2.3.04
Ichiro Shigkeawa
{"title":"Memories of Professor Hiroshi Kunita","authors":"Ichiro Shigkeawa","doi":"10.31390/josa.2.3.04","DOIUrl":"https://doi.org/10.31390/josa.2.3.04","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133867283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Works of Hiroshi Kunita in the Sixties 论六十年代国田浩的作品
Journal of Stochastic Analysis Pub Date : 2021-08-10 DOI: 10.31390/josa.2.3.03
M. Fukushima
{"title":"On the Works of Hiroshi Kunita in the Sixties","authors":"M. Fukushima","doi":"10.31390/josa.2.3.03","DOIUrl":"https://doi.org/10.31390/josa.2.3.03","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128909042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Berry-Esseen Bounds for Approximate Maximum Likelihood Estimators in the α-Brownian Bridge α-布朗桥中近似极大似然估计的Berry-Esseen界
Journal of Stochastic Analysis Pub Date : 2021-06-24 DOI: 10.31390/josa.2.2.08
Khalifa Es-Sebaiy, Jabrane Moustaaid, I. Ouassou
{"title":"Berry-Esseen Bounds for Approximate Maximum Likelihood Estimators in the α-Brownian Bridge","authors":"Khalifa Es-Sebaiy, Jabrane Moustaaid, I. Ouassou","doi":"10.31390/josa.2.2.08","DOIUrl":"https://doi.org/10.31390/josa.2.2.08","url":null,"abstract":"Let T > 0, α > 1 2 . In this work we consider the problem of estimating the drift parameter of the α-Brownian bridge defined as dXt = −α Xt T−tdt + dWt, 0 ≤ t < T , where W is a standard Brownian motion. Assume that the process X is observed equidistantly in time with the step size ∆n := T n+1 , ti = i∆n, i = 0, ..., n. We will propose two approximate maximum likelihood estimators α̂n and ᾱn for the drift parameter α based on the discrete observations Xti , i = 0, ..., n. The consistency of those estimators is studied. Explicit bounds for the Kolmogorov distance in the central limit theorem for the estimators α̂n and ᾱn are obtained.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1998 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123551603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Rough Paths and Regularization 粗糙路径和正则化
Journal of Stochastic Analysis Pub Date : 2021-06-15 DOI: 10.31390/JOSA.2.4.01
Andressa Gomes, A. Ohashi, F. Russo, Alan Teixeira
{"title":"Rough Paths and Regularization","authors":"Andressa Gomes, A. Ohashi, F. Russo, Alan Teixeira","doi":"10.31390/JOSA.2.4.01","DOIUrl":"https://doi.org/10.31390/JOSA.2.4.01","url":null,"abstract":"Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on deterministic techniques but there is still a probability in the background. The goal of this paper is to establish a connection between stochastically controlled-type processes, a concept reminiscent from rough paths theory, and the so-called weak Dirichlet processes. As a by-product, we present the connection between rough and Stratonovich integrals for cadlag weak Dirichlet processes integrands and continuous semimartingales integrators.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117269371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Linear Decomposition and Anticipating Integral for Certain Random Variables 一类随机变量的线性分解与预测积分
Journal of Stochastic Analysis Pub Date : 2021-03-01 DOI: 10.31390/JOSA.2.1.06
ching-tang wu, J. Yen
{"title":"Linear Decomposition and Anticipating Integral for Certain Random Variables","authors":"ching-tang wu, J. Yen","doi":"10.31390/JOSA.2.1.06","DOIUrl":"https://doi.org/10.31390/JOSA.2.1.06","url":null,"abstract":"In this paper, we construct an anticipating stochastic integral by linearly decompose a class of non Ft-measurable random variables. The result is applied to the derivation of the Itô formula.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121919408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixed Generalized Fractional Brownian Motion 混合广义分数布朗运动
Journal of Stochastic Analysis Pub Date : 2021-02-19 DOI: 10.31390/JOSA.2.2.02
E. Mliki, S. Alajmi
{"title":"Mixed Generalized Fractional Brownian Motion","authors":"E. Mliki, S. Alajmi","doi":"10.31390/JOSA.2.2.02","DOIUrl":"https://doi.org/10.31390/JOSA.2.2.02","url":null,"abstract":". To extend several known centered Gaussian processes, we intro- duce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. This process generalizes both the well-known mixed fractional Brownian motion introduced by Cheridito [7] and the generalized fractional Brownian motion introduced by Zili [29]. We study its main stochastic properties, its non-Markovian and non-stationarity characteristics and the conditions under which it is not a semimartingale. We prove the long-range dependence properties of this process.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126375601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Covariant Ergodic Quantum Markov Semigroups via Systems of Imprimitivity 非基系统中的协变遍历量子马尔可夫半群
Journal of Stochastic Analysis Pub Date : 2021-02-19 DOI: 10.31390/josa.2.4.07
R. Balu
{"title":"Covariant Ergodic Quantum Markov Semigroups via Systems of Imprimitivity","authors":"R. Balu","doi":"10.31390/josa.2.4.07","DOIUrl":"https://doi.org/10.31390/josa.2.4.07","url":null,"abstract":"We construct relativistic quantumMarkov semigroups from covariant completely positive maps. We proceed by generalizing a step in Stinespring’s dilation to a general system of imprimitivity and basing it on Poincarè group. The resulting noise channels are relativistically consistent and the method is applicable to any fundamental particle, though we demonstrate it for the case of light-like particles. The Krauss decomposition of the relativistically consistent completely positive identity preserving maps (our set up is in Heisenberg picture) enables us to construct the covariant quantum Markov semigroups that are uniformly continuous. We induce representations from the little groups to ensure the quantum Markov semigroups that are ergodic due to transitive systems imprimitivity.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"429 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114254071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noncentral Limit Theorem for Large Wishart Matrices with Hermite Entries 具有Hermite项的大Wishart矩阵的非中心极限定理
Journal of Stochastic Analysis Pub Date : 2021-02-05 DOI: 10.31390/JOSA.2.1.02
Charles-Philippe Diez, C. Tudor
{"title":"Noncentral Limit Theorem for Large Wishart Matrices with Hermite Entries","authors":"Charles-Philippe Diez, C. Tudor","doi":"10.31390/JOSA.2.1.02","DOIUrl":"https://doi.org/10.31390/JOSA.2.1.02","url":null,"abstract":". We analyze the limit behavior of the Wishart matrix W n,d = X n,d X Tn,d constructed from an n × d random matrix X n,d whose entries are given by the increments of the Hermite process. These entries are correlated on the same row, independent from one row to another and their probability distribution is di ff erent on di ff erent rows. We prove that the Wishart matrix converges in law, as d → ∞ , to a diagonal random matrix whose diagonal elements are random variables in the second Wiener chaos. We also estimate the Wasserstein distance associated to this convergence.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129206508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The Boundedness of General Alternative Singular Integrals with Respect to the Gaussian Measure 关于高斯测度的一般交替奇异积分的有界性
Journal of Stochastic Analysis Pub Date : 2020-12-14 DOI: 10.31390/JOSA.1.4.14
Eduardo Navas, E. Pineda, W. Urbina
{"title":"The Boundedness of General Alternative Singular Integrals with Respect to the Gaussian Measure","authors":"Eduardo Navas, E. Pineda, W. Urbina","doi":"10.31390/JOSA.1.4.14","DOIUrl":"https://doi.org/10.31390/JOSA.1.4.14","url":null,"abstract":"In this paper we introduce a new class of Gaussian singular integrals, the general alternative Gaussian singular integrals and study the boundedness of them in Lp( d), 1 < p < 1 and its weak (1, 1) boundedness with respect to the Gaussian measure following [7] and [1], respectively.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"31 4-5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132630374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Error Estimates for Discrete Approximations of Game Options with Multivariate Diffusion Asset Prices 具有多元扩散资产价格的博弈选项离散逼近的误差估计
Journal of Stochastic Analysis Pub Date : 2020-12-02 DOI: 10.31390/josa.2.3.08
Y. Kifer
{"title":"Error Estimates for Discrete Approximations of Game Options with Multivariate Diffusion Asset Prices","authors":"Y. Kifer","doi":"10.31390/josa.2.3.08","DOIUrl":"https://doi.org/10.31390/josa.2.3.08","url":null,"abstract":"We obtain error estimates for strong approximations of a diffusion with a diffusion matrix $sigma$ and a drift b by the discrete time process defined recursively X_N((n+1)/N) = X_N(n/N)+N^{1/2}sigma(X_N(n/N))xi(n+1)+N^{-1}b(XN(n/N)); where xi(n); ngeq 1 are i.i.d. random vectors, and apply this in order to approximate the fair price of a game option with a diffusion asset price evolution by values of Dynkin's games with payoffs based on the above discrete time processes. This provides an effective tool for computations of fair prices of game options with path dependent payoffs in a multi asset market with diffusion evolution.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126635692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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